| The first part of this thesis tells the story of the universe as an interplay between spins 0, 1 and 2. It is not a complete account and the level of detail is not uniform---there are gaps due to lack of understanding, and due to lack of time for LaTeX-ing notes. The parts I don't understand are missing pieces of the story about which I am uneasy, and I try to explain the discomfort. After a general and historical introduction, I review the framework in which modern theoretical physics takes place, namely lagrangian and hamiltonian mechanics, in the generality required to handle theories with gauge redundancy. I then discuss the global symmetry groups we demand of these systems. First is the galilean group, the symmetry group of the newtonian theory of gravity, but it is not the right group. Then comes the Poincare group, the one we see realized in nature, and I discuss its consequences for classical and quantum physics. The most important of these consequences is the limiting of possibilities for particle spins and interaction, which I review in separate chapters for spin-0, spin-1, and spin-2.;Next, I review cosmology as a solution to GR, and the acceleration of the universe. The accelerating universe reveals the cosmological constant problem, a severe quandary for our paradigm. I consider the possibility of modifying gravity to account for the acceleration, and see why some simple attempts fail.;The second part of the thesis contains original work in a series of attempts to address the cosmological constant problem. The first is a new way of looking at certain F(R) theories, where the cosmological constant appears as a redundant coupling, with the redundancy broken only by a small non-minimal coupling. This allows to shift the fine tuning of the cosmological constant into other sectors of the theory. Such a freedom is then used to write a theory based on Gauss-Bonnet gravity which realizes a technically natural tuning of the cosmological constant. The next chapter is an excursion into the lagrangian formalism and boundary terms. There is some subtlety in Gibbons-Hawking-York terms required of the actions of higher-derivative theories such as the F(R) theories, which had not been worked out in detail before. Here it is shown what the correct boundary terms must be.;The next attempt is to make the graviton massive. This attempt contains no original results, but it provides a good example of the things that go wrong when one tries to modify gravity away from GR. The tools developed will be useful later. The final attempt is to add extra dimensions. In particular, I review the Dvali-Gabadadze-Porrati (DGP) model, which can be thought of as a nicer way of making the graviton massive. I report on a new result: superluminal excitations are essentially unavoidable in the DGP model, and represent a challenge to any potential UV completion.;In the final chapter, I speculate that some of the things considered in this thesis, namely modified gravity and boundary conditions, might offer a solution to the arrow of time problem. The appendices catalog some often used formulae and facts. (Abstract shortened by UMI.)... |
